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Activity: Ship Speed and Efficiency

NGSS Science and Engineering Practices:

NGSS Crosscutting Concepts:


  • Table 8.9
  • Table 8.10
  • Long wave tank, 2 m or more
  • Pulley device on ring stand
  • Model ships < 30 cm (from Activity: Design a Ship)
  • Pencil
  • Scale or balance
  • Meter stick
  • 5 m length of string
  • Paper clip or fish hook
  • Four 10 g weights
  • Cup with handle
  • Stopwatch
  • Construction paper
  • Scissors
  • Towels


  1. Assemble the tow tank shown in Fig. 8.54 as follows:
    1. Obtain a wave tank at least 2 m long. Fill the tank with water to within 10 cm of the top edge.
    2. Set up the pulley device. Attach pulley no. 1 to the end of the tank. Attach pulley no. 2 to a ring stand.

<p><strong>Fig. 8.54.</strong> Tow tank</p><br />

  1. Determine the speeds of various ship models.
    1. Obtain at least four ships made in Activity: Design a Ship.
    2. Measure the weight (gf) of the ships and record these in Table 8.9. Measure the distance that each ship will travel in the tow tank from the bow tip to pulley no. 1.
    3. Beginning with the first boat, attach the towline to the bow of the ship. Place two 10 g weights in the cup to serve as a propulsion force. Release the ship. Measure the time in seconds that the ship takes to reach the other end of the tow tank. Record the data in Table 8.9.
    4. Compute the speed of the ship. Record the speed in Table 8.9.
    5. Repeat steps b–d for each of the other ships.
  2. Graph ship speed versus ship weight in Fig. 8.55 for each of your ships.

<p><strong>Fig. 8.55.</strong> Graph of ship speed versus ship weight</p><br />

  1. Make a watermarked picture profile of the waves formed by the ship as in Activity: Standing Waves.
    1. Have one partner hold a sheet of construction paper out of the path of the ship.
    2. Just as the stern of the boat passes the paper, quickly dip the paper in and out of the wake, the waves formed by the boat.
    3. Immediately pencil in the wake profile. Label the construction paper with the powering force (in grams) and your name.
  2. Repeat steps 2c and 2d using additional weights. Record the data in Table 8.10.
  3. Determine the efficiency of your ship at different speeds.
    1. Graph speed against powering force (in grams) in Fig. 8.56. Draw a smooth line connecting the data points.
    2. Place an “X” through the graph where the efficiency is highest. Efficiency is greatest when speed divided by powering force yields the largest value. (This is where the slope of the graph is steepest.)

<p><strong>Fig. 8.56.</strong> Ship speed plotted against powering force</p><br />

  1. Determine the effect of ship speed on wave size. The amount of water above and below the still-water level is a measure of wave size. It is also related to the energy in the waves.
    1. On each of the profiles you made in step 4, draw a straight line across the paper midway between crests and troughs of the waves using a meter stick. This line represents the still-water level. Darken the areas between the still-water level and the crests and troughs with a pencil (Fig. 8.57).
    2. For each profile, cut out the darkened area of the paper and determine its weight in grams. This is the wave energy index in grams.
    3. Graph ship speed against wave energy index in Fig. 8.58.

<p><strong>Fig. 8.57.</strong> Darkened wave profile</p><br />
<p><strong>Fig. 8.58.</strong> Ship speed plotted against wave energy index</p><br />


Activity Questions: 
  1. Which of the models traveled the fastest? Explain why you think one of the models had the fastest speed.
  2. What effect did ship weight and ship design have on ship speed?
  3. Does ship speed increase constantly as the powering force increases? Explain the reasoning for your answer.
  4. As ship speed increases, how is the size of waves (wake) affected? What is your evidence?
  5. Examine ship speed
    1. At what speed does each ship travel most efficiently?
    2. If you were building a small electric motor for each ship, what propulsion force would you have the motor exert to be the most fuel-efficient?
    3. What do you think of the following statement: Traveling at fuel-efficient speed is not always desirable in real situations.

The formula for work energy is:

  1. Make a graph similar to that in Fig. 8.56 displaying speed (cm/sec) vertically and energy (gf x cm) horizontally. Compare this graph with the graph in Fig. 8.58. Explain the differences and similarities between the graphs.
  2. Hypothesize whether there is a maximum speed that one of the ships could go. If so, what do you think it is? How did you arrive at this speed? How could you test your hypothesis?
  3. Compare the efficient hull speed of the ships. What relationship, if any, is there between
    1. efficient hull speed and hull length? 
    2. efficient hull speed and hull shape?
  4. Imagine that you are a ship or boat builder. Design an advertisement describing one of your ships. Use as many of the following terms as possible:
    1. design
    2. fuel efficiency
    3. speed (maximum speed)
    4. type of work or use
    5. stability
    6. cargo capacity (tonnage)
    7. powering force
    8. ship weight
    9. ship displacement
    10. length
    11. width (beam)
    12. price
  5. Variability is the amount of difference between the values in the data that you’ve collected. Was there high variability in your recorded wake heights? What about variability between your recorded measurements and a classmate’s measurements?
Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawaii, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.